by Ross Finney, George Thomas, Maurice Weir and Frank Giordano

Cover type:

Edition/Copyright: 10TH 03

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

Edition/Copyright: 10TH 03

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

Author Bio

**Thomas, George B. Jr. : Massachusetts Institute of Technology**

**Finney, Ross L. : Massachusetts Institute of Technology**

**Weir, Maurice D. : Naval Postgraduate School**

(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)

**P. Preliminaries. **Lines.

Functions and Graphs.

Exponential Functions.

Inverse Functions and Logarithms.

Trigonometric Functions and Their Inverses.

Parametric Equations.

Modeling Change.

Finding Limits and One-Sided Limits.

Limits Involving Infinity.

Continuity.

Tangent Lines.

The Derivative as a Rate of Change.

Derivatives of Products, Quotients, and Negative Powers.

Derivatives of Trigonometric Functions.

The Chain Rule.

Implicit Differentiation.

Related Rates.

The Mean Value Theorem and Differential Equations.

The Shape of a Graph.

Graphical Solutions of Autonomous Differential Equations.

Modeling and Optimization.

Linearization and Differentials.

Newton's Method.

Integral Rules; Integration by Substitution.

Estimating with Finite Sums.

Riemann Sums and Definite Integrals.

The Mean Value and Fundamental Theorems.

Substitution in Definite Integrals.

Numerical Integration.

Modeling Volume Using Cylindrical Shells.

Lengths of Plane Curves.

Springs, Pumping and Lifting.

Fluid Forces.

Moments and Centers of Mass.

Exponential Functions.

Derivatives of Inverse Trigonometric Functions; Integrals.

First-Order Separable Differential Equations.

Linear First-Order Differential Equations.

Euler's Method; Population Models.

Hyperbolic Functions.

Integration by Parts.

Partial Fractions.

Trigonometric Substitutions.

Integral Tables, Computer Algebra Systems, and Monte Carlo Integration.

L'Hôpital's Rule.

Improper Integrals.

Subsequences, Bounded Sequences, and Picard's Method.

Infinite Series.

Series of Nonnegative Terms.

Alternating Series, Absolute and Conditional Convergence.

Power Series.

Taylor and Maclaurin Series.

Applications of Power Series.

Fourier Series.

Fourier Cosine and Sine Series.

Dot Products.

Vector-Valued Functions.

Modeling Projectile Motion.

Polar Coordinates and Graphs.

Calculus of Polar Curves.

Dot and Cross Products.

Lines, and Planes in Space.

Cylinders and Quadric Surfaces.

Vector-Valued Functions and Space Curves.

Arc Length and the Unit Tangent Vector T.

The TNB Frame; Tangential and Normal Components of Acceleration.

Planetary Motion and Satellites.

Limits and Continuity in Higher Dimensions.

Partial Derivatives.

The Chain Rule.

Directional Derivatives, Gradient Vectors, and Tangent Planes.

Linearization and Differentials.

Extreme Values and Saddle Points.

Lagrange Multipliers.

Partial Derivatives with Constrained Variables.

Taylor's Formula for Two Variables.

Areas, Moments, and Centers of Mass.

Double Integrals in Polar Form.

Triple Integrals in Rectangular Coordinates.

Masses and Moments in Three Dimensions.

Triple Integrals in Cylindrical and Spherical Coordinates.

Substitutions in Multiple Integrals.

Vector Fields, Work, Circulation, and Flux.

Path Independence, Potential Functions, and Conservative Fields.

Green's Theorem in the Plane.

Surface Area and Surface Integrals.

Parametrized Surfaces.

Stokes' Theorem.

Divergence Theorem and a Unified Theory.

Ross Finney, George Thomas, Maurice Weir and Frank Giordano

Cover type:Edition/Copyright: 10TH 03

Publisher: Addison-Wesley Longman, Inc.

Published: 2003

International: No

Author Bio

**Thomas, George B. Jr. : Massachusetts Institute of Technology**

**Finney, Ross L. : Massachusetts Institute of Technology**

**Weir, Maurice D. : Naval Postgraduate School**

Table of Contents

(Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter.)

**P. Preliminaries. **Lines.

Functions and Graphs.

Exponential Functions.

Inverse Functions and Logarithms.

Trigonometric Functions and Their Inverses.

Parametric Equations.

Modeling Change.

Finding Limits and One-Sided Limits.

Limits Involving Infinity.

Continuity.

Tangent Lines.

The Derivative as a Rate of Change.

Derivatives of Products, Quotients, and Negative Powers.

Derivatives of Trigonometric Functions.

The Chain Rule.

Implicit Differentiation.

Related Rates.

The Mean Value Theorem and Differential Equations.

The Shape of a Graph.

Graphical Solutions of Autonomous Differential Equations.

Modeling and Optimization.

Linearization and Differentials.

Newton's Method.

Integral Rules; Integration by Substitution.

Estimating with Finite Sums.

Riemann Sums and Definite Integrals.

The Mean Value and Fundamental Theorems.

Substitution in Definite Integrals.

Numerical Integration.

Modeling Volume Using Cylindrical Shells.

Lengths of Plane Curves.

Springs, Pumping and Lifting.

Fluid Forces.

Moments and Centers of Mass.

Exponential Functions.

Derivatives of Inverse Trigonometric Functions; Integrals.

First-Order Separable Differential Equations.

Linear First-Order Differential Equations.

Euler's Method; Population Models.

Hyperbolic Functions.

Integration by Parts.

Partial Fractions.

Trigonometric Substitutions.

Integral Tables, Computer Algebra Systems, and Monte Carlo Integration.

L'Hôpital's Rule.

Improper Integrals.

Subsequences, Bounded Sequences, and Picard's Method.

Infinite Series.

Series of Nonnegative Terms.

Alternating Series, Absolute and Conditional Convergence.

Power Series.

Taylor and Maclaurin Series.

Applications of Power Series.

Fourier Series.

Fourier Cosine and Sine Series.

Dot Products.

Vector-Valued Functions.

Modeling Projectile Motion.

Polar Coordinates and Graphs.

Calculus of Polar Curves.

Dot and Cross Products.

Lines, and Planes in Space.

Cylinders and Quadric Surfaces.

Vector-Valued Functions and Space Curves.

Arc Length and the Unit Tangent Vector T.

The TNB Frame; Tangential and Normal Components of Acceleration.

Planetary Motion and Satellites.

Limits and Continuity in Higher Dimensions.

Partial Derivatives.

The Chain Rule.

Directional Derivatives, Gradient Vectors, and Tangent Planes.

Linearization and Differentials.

Extreme Values and Saddle Points.

Lagrange Multipliers.

Partial Derivatives with Constrained Variables.

Taylor's Formula for Two Variables.

Areas, Moments, and Centers of Mass.

Double Integrals in Polar Form.

Triple Integrals in Rectangular Coordinates.

Masses and Moments in Three Dimensions.

Triple Integrals in Cylindrical and Spherical Coordinates.

Substitutions in Multiple Integrals.

Vector Fields, Work, Circulation, and Flux.

Path Independence, Potential Functions, and Conservative Fields.

Green's Theorem in the Plane.

Surface Area and Surface Integrals.

Parametrized Surfaces.

Stokes' Theorem.

Divergence Theorem and a Unified Theory.